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Simplifying 50 + 90t + -4.9t2 = 250 Solving 50 + 90t + -4.9t2 = 250 Solving for variable 't'. Reorder the terms: 50 + -250 + 90t + -4.9t2 = 250 + -250 Combine like terms: 50 + -250 = -200 -200 + 90t + -4.9t2 = 250 + -250 Combine like terms: 250 + -250 = 0 -200 + 90t + -4.9t2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 40.81632653 + -18.36734694t + t2 = 0 Move the constant term to the right: Add '-40.81632653' to each side of the equation. 40.81632653 + -18.36734694t + -40.81632653 + t2 = 0 + -40.81632653 Reorder the terms: 40.81632653 + -40.81632653 + -18.36734694t + t2 = 0 + -40.81632653 Combine like terms: 40.81632653 + -40.81632653 = 0.00000000 0.00000000 + -18.36734694t + t2 = 0 + -40.81632653 -18.36734694t + t2 = 0 + -40.81632653 Combine like terms: 0 + -40.81632653 = -40.81632653 -18.36734694t + t2 = -40.81632653 The t term is -18.36734694t. Take half its coefficient (-9.18367347). Square it (84.33985840) and add it to both sides. Add '84.33985840' to each side of the equation. -18.36734694t + 84.33985840 + t2 = -40.81632653 + 84.33985840 Reorder the terms: 84.33985840 + -18.36734694t + t2 = -40.81632653 + 84.33985840 Combine like terms: -40.81632653 + 84.33985840 = 43.52353187 84.33985840 + -18.36734694t + t2 = 43.52353187 Factor a perfect square on the left side: (t + -9.18367347)(t + -9.18367347) = 43.52353187 Calculate the square root of the right side: 6.597236684 Break this problem into two subproblems by setting (t + -9.18367347) equal to 6.597236684 and -6.597236684.Subproblem 1
t + -9.18367347 = 6.597236684 Simplifying t + -9.18367347 = 6.597236684 Reorder the terms: -9.18367347 + t = 6.597236684 Solving -9.18367347 + t = 6.597236684 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.18367347' to each side of the equation. -9.18367347 + 9.18367347 + t = 6.597236684 + 9.18367347 Combine like terms: -9.18367347 + 9.18367347 = 0.00000000 0.00000000 + t = 6.597236684 + 9.18367347 t = 6.597236684 + 9.18367347 Combine like terms: 6.597236684 + 9.18367347 = 15.780910154 t = 15.780910154 Simplifying t = 15.780910154Subproblem 2
t + -9.18367347 = -6.597236684 Simplifying t + -9.18367347 = -6.597236684 Reorder the terms: -9.18367347 + t = -6.597236684 Solving -9.18367347 + t = -6.597236684 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.18367347' to each side of the equation. -9.18367347 + 9.18367347 + t = -6.597236684 + 9.18367347 Combine like terms: -9.18367347 + 9.18367347 = 0.00000000 0.00000000 + t = -6.597236684 + 9.18367347 t = -6.597236684 + 9.18367347 Combine like terms: -6.597236684 + 9.18367347 = 2.586436786 t = 2.586436786 Simplifying t = 2.586436786Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.780910154, 2.586436786}
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